Questions from General Calculus


Q: Let f (x) = 1 - x2/3.

Let f (x) = 1 - x2/3. Show that f (-1) = f (1) but there is no number c in (-1, 1) such that f ‘(c) = 0. Why does this not contradict Rolle’s Theorem?

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Q: Let f (x) = tan x. Show that f

Let f (x) = tan x. Show that f (0) = f (π) but there is no number c in (0, π) such that f ‘(c) = 0. Why does this not contradict Rolle’s Theorem?

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Q: Verify that the function satisfies the hypotheses of the Mean Value Theorem

Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. f (x) = 2x2 - 3x + 1,...

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Q: Verify that the function satisfies the hypotheses of the Mean Value Theorem

Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. f (x) = x3 - 3x + 2, [...

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Q: Verify that the function satisfies the hypotheses of the Mean Value Theorem

Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. f (x) = ln x, [1, 4]

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Q: Verify that the function satisfies the hypotheses of the Mean Value Theorem

Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given interval. Then find all numbers c that satisfy the conclusion of the Mean Value Theorem. f (x) = 1/x, [1, 3]

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Q: Find the number c that satisfies the conclusion of the Mean Value

Find the number c that satisfies the conclusion of the Mean Value Theorem on the given interval. Graph the function, the secant line through the endpoints, and the tangent line at (c, f(c)). Are the s...

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Q: Let f (x) = ( x – 3)-2

Let f (x) = ( x – 3)-2. Show that there is no value of c in (1, 4) such that f (4) - f (1) = f ‘(c)(4 – 1). Why does this not contradict the Mean Value Theorem?

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Q: The biomass B(t) of a fish population is the

The biomass B(t) of a fish population is the total mass of the members of the population at time t. It is the product of the number of individuals N(t) in the population and the average mass M(t) of a...

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Q: Let f (x) = 2 - |2x - 1

Let f (x) = 2 - |2x - 1|. Show that there is no value of c such that f (3) - f (0) = f ‘(c)(3 – 0). Why does this not contradict the Mean Value Theorem?

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